3-D acoustic analysis of elliptical chamber mufflers having an end-inlet and a side-outlet: An impedance matrix approach

The acoustical behavior of an elliptical chamber muffler having an end-inlet and side-outlet port is analyzed semi-analytically. A uniform piston source is assumed to model the 3-D acoustic field in the elliptical chamber cavity. Towards this end, we consider the modal expansion of acoustic pressure field in the elliptical cavity in terms of angular and radial Mathieu functions, subjected to rigid wall condition, whereupon under the assumption of a point source, Green's function is obtained. On integrating this function over piston area of the side or end port and dividing it by piston area, one obtains the acoustic field, whence one can find the impedance matrix parameters characterizing the 2-port system. The acoustic performance of these configurations is evaluated in terms of transmission loss (TL). The analytical results thus obtained are compared with 3-D HA carried on a commercial software for certain muffler configurations. These show excellent agreement, thereby validating the 3-D semi-analytical piston driven model. The influence of the chamber length as well as the angular and axial location of the end and side ports on TL performance is also discussed, thus providing useful guidelines to the muffler designer. (c) 2011 Elsevier B.V. All rights reserved.

Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.

DEVELOPMENT OF A LOW COST IMPEDANCE TUBE TO MEASURE THE ACOUSTIC ABSORPTION AND TRANSMISSION LOSS OF MATERIALS

Traditional methods of measuring sound absorption coefficient and sound transmission loss of a material are time consuming. To overcome this limitation, normal incidence sound absorption and transmission loss measurement technique was developed. Unfortunately the equipment required for this task is equally expensive. Hence efforts are taken to develop a cost-effective equipment for measuring normal incidence sound absorption coefficient and transmission loss. An impedance tube capable of measure absorption coefficient and transmission loss is designed and built under a budget of $1500 for educational institutes. A background study is performed to gain knowledge and understanding of the normal incidence measurements technique. Based on the literature review, parameters involved such as tube material, source and microphone properties, sample holders, etc. are discussed in depth. Based on these parameters, design options are generated to meet the cost and functionality targets pre-assigned. After selection of materials and components, an impedance tube is built and tested using three fibrous absorption materials for absorption and a barrier for transmission loss performance. These measured results then compared with those obtained with the help of industry recognized Brüel & Kjær impedance tube. The results show performances are comparable, hence validation the new built tube.

A method for the experimental evaluation of the acoustic characteristics of an engine exhaust system in the presence of mean flow

The paper deals with an exact analysis of standing waves in an impedance tube with mean flow. A method is offered for the experimental evaluation of the various wave parameters. Navier–Stokes equations have been solved for evaluating the volume velocity taking into account mean flow, viscosity, etc. The engine exhaust system has been characterized as an acoustic source with an acoustic pressure and internal impedance. A method is suggested for the evaluation of these hypothetical parameters using the exhaust pipe as an impedance tube.Subject Classification: [43]85.20; [43]20.40.

On uniqueness, transfer and combination of acoustic sources in one-dimensional systems

The use of electroacoustic analogies suggests that a source of acoustical energy (such as an engine, compressor, blower, turbine, loudspeaker, etc.) can be characterized by an acoustic source pressure ps and internal source impedance Zs, analogous to the open-circuit voltage and internal impedance of an electrical source. The present paper shows analytically that the source characteristics evaluated by means of the indirect methods are independent of the loads selected; that is, the evaluated values of ps and Zs are unique, and that the results of the different methods (including the direct method) are identical. In addition, general relations have been derived here for the transfer of source characteristics from one station to another station across one or more acoustical elements, and also for combining several sources into a single equivalent source. Finally, all the conclusions are extended to the case of a uniformly moving medium, incorporating the convective as well as dissipative effects of the mean flow.

Acoustic performance of hoses - A parametric study

Modeling of wave propagation in hoses, unlike in rigid pipes or waveguides, introduces a coupling between the inside medium, the hose wall, and the outside medium, This alters the axial wave number and thence the corresponding effective speed of sound inside the hose resulting in sound radiation into the outside medium, also called the breakout or shell noise, The existing literature on the subject is such that a hose cannot be integrated into the,whole piping system made up of sections of hoses, pipes, and mufflers to predict the acoustical performance in terms of transmission loss (TL), The present paper seeks to fill this gap, Three one-dimensional coupled wave equations are written to account for the presence of a yielding wall with a finite lumped transverse impedance of the hose material, The resulting wave equation can readily be reduced to a transfer matrix form using an effective wave number for a moving medium in a hose section, Incorporating the effect of fluid loading due to the outside medium also allows prediction of the transverse TL and the breakout noise, Axial TL and transverse TL have been combined into net TL needed by designers, Predictions of the axial as well as transverse TL are shown to compare well with those of a rigorous 3-D analysis using only one-hundredth of the computation time, Finally, results of some parametric studies are reported for engineers involved in the acoustical design of hoses. (C) 1996 Institute of Noise Control Engineering.

Authors reply to "On uniqueness, transfer and combination of acoustic sources in one-dimensional systems"

The use of electroacoustic analogies suggests that a source of acoustical energy (such as an engine, compressor, blower, turbine, loudspeaker, etc.) can be characterized by an acoustic source pressure ps and internal source impedance Zs, analogous to the open-circuit voltage and internal impedance of an electrical source. The present paper shows analytically that the source characteristics evaluated by means of the indirect methods are independent of the loads selected; that is, the evaluated values of ps and Zs are unique, and that the results of the different methods (including the direct method) are identical. In addition, general relations have been derived here for the transfer of source characteristics from one station to another station across one or more acoustical elements, and also for combining several sources into a single equivalent source. Finally, all the conclusions are extended to the case of a uniformly moving medium, incorporating the convective as well as dissipative effects of the mean flow.

Three-dimensional acoustic analysis of an elliptical chamber muffler with a side inlet and a side outlet

The acoustical behaviour of an elliptical chamber muffler having a side inlet and side outlet port is analyzed in this paper, wherein a uniform velocity piston source is assumed to model the 3-D acoustic field in the elliptical chamber cavity. Towards this end, we consider the modal expansion of the acoustic pressure field in the elliptical cavity in terms of the angular and radial Mathieu func-tions, subjected to the rigid wall condition. Then, the Green's function due to the point source lo-cated on the side (curved) surface of the elliptical chamber is obtained. On integrating this function over the elliptical piston area on the curved surface of the elliptical chamber and subsequent divi-sion by the area of the elliptic piston, one obtains the acoustic pressure field due to the piston driven source which is equivalent to considering plane wave propagation in the side ports. Thus, one can obtain the acoustic pressure response functions, i.e., the impedance matrix (Z) parameters due to the sources (ports) located on the side surface, from which one may also obtain a progressive wave rep-resentation in terms of the scattering matrix (S). Finally, the acoustic performance of the muffler is evaluated in terms of the Transmission loss (TL) which is computed in terms of the scattering pa-rameters. The effect of the axial length of the muffler and the angular location of the ports on the TL characteristics is studied in detail. The acoustically long chambers show dominant axial plane wave propagation while the TL spectrum of short chambers indicates the dominance of the trans-versal modes. The 3-D analytical results are compared with the 3-D FEM simulations carried on a commercial software and are shown to be in an excellent agreement, thereby validating the analyti-cal procedure suggested in this work.

Models for acoustic propagation through turbofan exhaust flows-lined ducts

Turbomachinery noise radiating into the rearward arc is an important problem. This noise is scattered by the trailing edges of the nacelle and the jet exhaust, and interacts with the shear layers between the external flow, bypass stream and jet, en route to the far field. In the past a range of relevant model problems involving semi-infinite cylinders have been solved. However, one limitation of these previous solutions is that they do not allow for the jet nozzle protruding a finite distance beyond the end of the nacelle (or in certain configurations being buried a finite distance upstream). With this in mind, we have used the matrix Wiener-Hopf technique to allow precisely this finite nacelle-jet nozzle separation to be included. We have previously reported results for the case of hard-walled ducts, which requires factorisation of a 2 × 2 matrix. In this paper we extend this work by allowing one of the duct walls, in this case the outer wall of the jet pipe, to be acoustically lined. This results in the need to factorise a 3 × 3 matrix, which is completed by use of a combination of pole-removal and Pad́e approximant techniques. Sample results are presented, investigating in particular the effects of exit plane stagger and liner impedance. Here we take the mean flow to be zero, but extension to nonzero Mach numbers in the core and bypass flow has also been completed. Copyright © 2009 by Nigel Peake & Ben Veitch.

Methods of multiparameter inversion of seismic data using the acoustic and elastic born approximations

This thesis presents two different forms of the Born approximations for acoustic and elastic wavefields and discusses their application to the inversion of seismic data. The Born approximation is valid for small amplitude heterogeneities superimposed over a slowly varying background. The first method is related to frequency-wavenumber migration methods. It is shown to properly recover two independent acoustic parameters within the bandpass of the source time function of the experiment for contrasts of about 5 percent from data generated using an exact theory for flat interfaces. The independent determination of two parameters is shown to depend on the angle coverage of the medium. For surface data, the impedance profile is well recovered.

The second method explored is mathematically similar to iterative tomographic methods recently introduced in the geophysical literature. Its basis is an integral relation between the scattered wavefield and the medium parameters obtained after applying a far-field approximation to the first-order Born approximation. The Davidon-Fletcher-Powell algorithm is used since it converges faster than the steepest descent method. It consists essentially of successive backprojections of the recorded wavefield, with angular and propagation weighing coefficients for density and bulk modulus. After each backprojection, the forward problem is computed and the residual evaluated. Each backprojection is similar to a before-stack Kirchhoff migration and is therefore readily applicable to seismic data. Several examples of reconstruction for simple point scatterer models are performed. Recovery of the amplitudes of the anomalies are improved with successive iterations. Iterations also improve the sharpness of the images.

The elastic Born approximation, with the addition of a far-field approximation is shown to correspond physically to a sum of WKBJ-asymptotic scattered rays. Four types of scattered rays enter in the sum, corresponding to P-P, P-S, S-P and S-S pairs of incident-scattered rays. Incident rays propagate in the background medium, interacting only once with the scatterers. Scattered rays propagate as if in the background medium, with no interaction with the scatterers. An example of P-wave impedance inversion is performed on a VSP data set consisting of three offsets recorded in two wells.

Analytical approximations for the modal acoustic impedances of simply supported, rectangular plates.

Coupling of the in vacuo modes of a fluid-loaded, vibrating structure by the resulting acoustic field, while known to be negligible for sufficiently light fluids, is still only partially understood. A particularly useful structural geometry for the study of this problem is the simply supported, rectangular flat plate, since it exhibits all the relevant physical features while still admitting an analytical description of the modes. Here the influence of the fluid can be expressed in terms of a set of doubly infinite integrals over wave number: the modal acoustic impedances. Closed-form solutions for these impedances do not exist and, while their numerical evaluation is possible, it greatly increases the computational cost of solving the coupled system of modal equations. There is thus a need for accurate analytical approximations. In this work, such approximations are sought in the limit where the modal wavelength is small in comparison with the acoustic wavelength and the plate dimensions. It is shown that contour integration techniques can be used to derive analytical formulas for this regime and that these formulas agree closely with the results of numerical evaluations. Previous approximations [Davies, J. Sound Vib. 15(1), 107-126 (1971)] are assessed in the light of the new results and are shown to give a satisfactory description of real impedance components, but (in general) erroneous expressions for imaginary parts.

Eccentricity effects on acoustic radiation from a spherical source suspended within a thermoviscous fluid sphere.

Acoustic radiation from a spherical source undergoing angularly periodic axisymmetric harmonic surface vibrations while eccentrically suspended within a thermoviscous fluid sphere, which is immersed in a viscous thermally conducting unbounded fluid medium, is analyzed in an exact fashion. The formulation uses the appropriate wave-harmonic field expansions along with the translational addition theorem for spherical wave functions and the relevant boundary conditions to develop a closed-form solution in form of infinite series. The analytical results are illustrated with a numerical example in which the vibrating source is eccentrically positioned within a chemical fluid sphere submerged in water. The modal acoustic radiation impedance load on the source and the radiated far-field pressure are evaluated and discussed for representative values of the parameters characterizing the system. The proposed model can lead to a better understanding of dynamic response of an underwater acoustic lens. It is equally applicable in miniature transducer analysis and design with applications in medical ultrasonics.

Microfluidics-based acoustic microbubble biosensor

This paper proposes a chip-scale microbubble-based biosensing platform. An encapsulated microbubble oscillates acoustically in liquid when exposed to an ultrasound field with its resonant frequency set by shell parameters. Changes in the resonant frequency of the microbubble can be used to monitor analyte-binding events on the shell. A device concept is proposed where ultrasonic transducers are integrated within a microfluidic channel, inside which electrodes are patterned for differential measurements of microbubble impedance. This device enables simultaneous measurements of the acoustic and electrical response of the microbubble, from which both mechanical and electrical parameters can be extracted. These parameters are used to provide a signature of the analyte. This paper presents acoustic and electrical models of the microbubbles, with the effect of shell parameters being thoroughly discussed. © 2013 IEEE.

SCANNING ACOUSTIC MICROSCOPE FOR CHARACTERIZATION OF ARTERIAL PLAQUE

Unstable arterial plaque is likely the key component of atherosclerosis, a disease which is responsible for two-thirds of heart attacks and strokes, leading to approximately 1 million deaths in the United States. Ultrasound imaging is able to detect plaque but as of yet is not able to distinguish unstable plaque from stable plaque. In this work a scanning acoustic microscope (SAM) was implemented and validated as tool to measure the acoustic properties of a sample. The goal for the SAM is to be able to provide quantitative measurements of the acoustic properties of different plaque types, to understand the physical basis by which plaque may be identified acoustically. The SAM consists of a spherically focused transducer which operates in pulse-echo mode and is scanned in a 2D raster pattern over a sample. A plane wave analysis is presented which allows the impedance, attenuation and phase velocity of a sample to be de- termined from measurements of the echoes from the front and back of the sample. After the measurements, the attenuation and phase velocity were analysed to ensure that they were consistent with causality. The backscatter coefficient of the samples was obtained using the technique outlined by Chen et al [8]. The transducer used here was able to determine acoustic properties from 10-40 MHz. The results for the impedance, attenuation and phase velocity were validated for high and low-density polyethylene against published results. The plane wave approximation was validated by measuring the properties throughout the focal region and throughout a range of incidence angles from the transducer. The SAM was used to characterize a set of recipes for tissue-mimicking phantoms which demonstrate indepen- dent control over the impedance, attenuation, phase velocity and backscatter coefficient. An initial feasibility study on a human artery was performed.